Calculating the infrared spectra of hot astrophysical molecules SELAC, May 2005 Jonathan Tennyson University College London

Layers in a star: the Sun

Spectrum of a hot star: black body-like

Infra red spectrum of an M-dwarf star

Cool stellar atmospheres : dominated by molecular absorption Brown Dwarf M-dwarf The molecular opacity problem (  m)

Cool stars: T = 2000 – 4000 K Thermodynamics equilibrium, 3-body chemistry C and O combine rapidly to form CO. M-Dwarfs: Oxygen rich, n(O) > n(C) H 2, H 2 O, TiO, ZrO, etc also grains at lower T C-stars: Carbon rich, n(C) > n(O) H 2, CH 4, HCN, C 3, HCCH, CS, etc S-Dwarfs: n(O) = n(C) Rare. H 2, FeH, MgH, no polyatomics Also (primordeal) ‘metal-free’ stars H, H 2, He, H , H 3 + only at low T

Also sub-stellar objects: CO less important Brown Dwarfs: T ~ 1500 K H 2, H 2 O, CH 4 T-Dwarfs: T ~ 1000K ‘methane stars’ How common are these? Deuterium burning test using HDO? Burn D only No nuclear synthesis

Modeling the spectra of cool stars Spectra very dense – cannot get T from black-body fit. Synthetic spectra require huge databases > 10 6 vibration-rotation transitions per triatomic molecule Sophisticated opacity sampling techniques. Partition functions also important Data distributed by R L Kururz (Harvard), see kurucz.harvard.edu

Physics of molecular opacities: Closed Shell diatomics CO, H 2, CS, etc Vibration-rotation transitions. Sparse: ~10,000 transitions Generally well characterized by lab data and/or theory (H 2 transitions quadrupole only) HeH +

Physics of molecular opacities: Open Shell diatomics TiO, ZrO, FeH, etc Low-lying excited states. Electronic-vibration-rotation transitions Dense: ~10,000,000 transitions (?) TiO now well understood using mixture of lab data and theory

Physics of molecular opacities: Polyatomic molecules H 2 O, HCN, H 3 +, C 3, CH 4, HCCH, etc Vibration-rotation transitions Very dense: 10,000,000 – 100,000,000 Impossible to characterize in the lab Detailed theoretical calculations Computed opacities exist for: H 2 O, HCN, H 3 +

Ab initio calculation of rotation-vibration spectra

The DVR3D program suite : triatomic vibration-rotation spectra Potential energy Surface,V(r 1,r 2,  ) Dipole function  (r 1,r 2,  ) J Tennyson, MA Kostin, P Barletta, GJ Harris OL Polyansky, J Ramanlal & NF Zobov Computer Phys. Comm. 163, 85 (2004).

Potentials: Ab initio or Spectroscopically determined

H 3 + H 2 O H 2 S HCN/HNC HeH + Molecule considered at high accuracy

Partition functions are important Model of cool, metal-free magnetic white dwarf WD by Pierre Bergeron (Montreal) Is the partition function of H 3 + correct?

Partition functions are important Model of WD using ab initio H 3 + partition function of Neale & Tennyson (1996)

HCN opacity, Greg Harris High accuracy ab initio potential and dipole surfaces Simultaneous treatment of HCN and HNC Vibrational levels up to cm -1 Rotational levels up to J=60 Calculations used SG Origin 2000 machine 200,000,000 lines computed Took 16 months Partition function estimates suggest 93% recovery of opacity at 3000 K

Ab initio vs. laboratory HNC bend fundamental (462.7 cm -1 ). Q and R branches visible. Slight displacement of vibrational band centre (2.5 cm -1 ). Good agreement between rotational spacing. Good agreement in Intensity distribution. Q branches of hot bands visible. Burkholder et al., J. Mol. Spectrosc. 126, 72 (1987)

GJ Harris, YV Pavlenko, HRA Jones & J Tennyson, MNRAS, 344, 1107 (2003).

Importance of water spectra Other Models of the Earth’s atmosphere Major combustion product (remote detection of forest fires, gas turbine engines) Rocket exhaust gases: H 2 + ½ O 2 H 2 O (hot) Lab laser and maser spectra Astrophysics Third most abundant molecule in the Universe (after H 2 & CO) Atmospheres of cool stars Sunspots Water masers Ortho-para interchange timescales

Sunspots Image from SOHO : 29 March 2001 Molecules on the Sun T=5760K Diatomics H 2, CO, CH, OH, CN, etc Sunspots T=3200K H 2, H 2 O, CO, SiO

Sunspot lab Sunspot: N-band spectrum L Wallace, P Bernath et al, Science, 268, 1155 (1995)

Assigning a spectrum with 50 lines per cm -1 1.Make ‘trivial’ assignments (ones for which both upper and lower level known experimentally) 2. Unzip spectrum by intensity 6 – 8 % absorption strong lines 4 – 6 % absorption medium 2 – 4 % absorption weak < 2 % absorption grass (but not noise) 3. Variational calculations using ab initio potential Partridge & Schwenke, J. Chem. Phys., 106, 4618 (1997) + adiabatic & non-adiabatic corrections for Born-Oppenheimer approximation 4. Follow branches using ab initio predictions branches are similar transitions defined by J – K a = n a or J – K c = n c, n constant Only strong/medium lines assigned so far OL Polyansky, NF Zobov, S Viti, J Tennyson, PF Bernath & L Wallace, Science, 277, 346 (1997).

Sunspot lab Assignments Sunspot: N-band spectrum L-band, K-band & H-band spectra also assigned Zobov et al, Astrophys. J., 489, L205 (1998); 520, 994 (2000); 577, 496 (2002).

Assignments using branches Ab initio potential Less accurate but extrapolate well J Error / cm -1 Determined potential Spectroscopically Variational calculations: Accurate but extrapolate poorly

Observed Ludwig Jorgensen Miller & Tennyson Spectrum of M-dwarf star TVLM 513 Water opacities HRA Jones, S Viti, S Miller, J Tennyson, F Allard & PH Hauschildt (1996)

Viti & Tennyson computed VT2 linelist: All vibration-rotation levels up to 30,000 cm -1 Giving ~ 7 x 10 8 transitions Similar study by Partridge & Schwenke (PS), NASA Ames New study by Barber & Tennyson (BT1/BT2) Computed Water opacity Variational nuclear motion calculations High accuracy potential energy surface Ab initio dipole surface

Spectroscopically determined water potentials ReferenceYear  vib /cm -1 N vib E max /cm -1 Hoy, Mills & Strey Carter & Handy Halonen & Carrington Jensen Polyansky et al (PJT1) Polyansky et al (PJT2) Partridge & Schwenke Shirin et al  mportant to treat vibrations and rotations

Emission spectra of comet 153P/Ikeya-Zhang (C/2002 C1) N. Dello Russo et al, Icarus, 168, 186 (2004) & Astrophys. J., 621, 537 (2005) Gives rotational temperatures Rotational temperatures & ortho/para ratios Solar pumping Emission lines

Water in Mira Cooler than sunspot, but what is T? v r = 92 km s -1

Nova V838 Mon Exploded Feb 2002

DPK Banerjee, R.J. Barber, N.K. Ashok & J. Tennyson, Astrophys. J. Lett (submitted).

Water assignments using variational calculations Long pathlength absoption (T = 296K) cm -1 Fourier Transform and Cavity Ring Down Laboratory emisson spectra (T =1300  1800K) 400 – 6000 cm -1 Absorption in sunspots (T = 3200 K) N band, L band, K band, H band  m 3  m 2  m 1.4  m  new lines assigned Dataset of measured H 2 16 O energy levels J. Tennyson, N.F. Zobov, R. Williamson, O.L. Polyansky & P.F. Bernath, J. Phys. Chem. Ref. Data, 30, 735 (2001). New: lab torch spectra (T ~ 3000 K) from Bernath lines.

Bob Barber Greg Harris T heoretical A tomic and M olecular P hysics and A strophysics

Accuracy better than 1cm  1 Adiabatic or Born-Oppenheimer Diagonal Correction (BODC) Non-adiabatic corrections for vibration and rotation Electronic (kinetic) relativistic effect Relativistic Coulomb potential (Breit effect) Radiative correction (Lamb shift or qed) Can BO electronic structure calculations be done this accurately? Variational rotation-vibration calculations with exact kinetic energy operator accurate to better than cm  1

mode E obs / cm -1 BO +  V ad  0.11   1.30    0.30   1.40   1.46   0.47    1.04    0.74  0.18 Ab initio vibrational band origins H2D+H2D+ H3+H3+ D2H+D2H+

mode E obs / cm  1 BO +  V ad  v   nuc  0.11   1.30    0.30   1.40   1.46  0.36   0.47  0.25    1.04    0.74  0.18  Ab initio vibrational band origins H2D+H2D+ H3+H3+ D2H+D2H+ O.L. Polyansky and J. Tennyson, J. Chem. Phys., 110, 5056 (1999).

J K a K c J K a K c E obs / cm -1 BO +  V ad  v   nuc + K NBO                                    H 2 D + : ab initio spectra

Obs / cm  1 5Z 1 6Z 1 CBS 2 CBS+CV 3 (010)  2.99  2.30  (020)  4.22  2.38  (030)  6.30  3.24  (040)  9.81  5.54  (050)   9.19  (101)  5.35 (201)  7.47 (301)  8.97 (401)  (501)   [104]  all  7.85 Ab initio calculations for water 1 MRCI calculation with Dunning’s aug-cc-pVnZ basis set 2 Extrapolation to Complete Basis Set (CBS) limit 3 Core—Valence (CV) correction OL Polyansky, AG Csaszar, J Tennyson, P Barletta, SV Shirin, NF Zobov, DW Schwenke & PJ Knowles Science, 299, 539 (2003)

BO / cm  1 +BODC 1 + Non-adiabatic  v   nuc 2 diag 3 full 4 (010)  0.46  0.19  0.06  0.07 (020)  0.94  0.38  0.12  0.15 (100)  0.55  0.46  0.72  0.70 (030)  1.43  0.55  0.18  0.23 (110)  0.16  0.65  0.77  0.76 (040)  2.00  0.71  0.23  0.30 (120)  0.23  0.83  0.83  0.84 (200)  1.25  0.88  1.39  1.37 (002)  1.47  0.90  1.47  1.57 (050)  2.71  0.84  0.28  0.32 Born-Oppenheimer corrections for water 1 Born-Oppenheimer diagonal correction using CASSCF wavefunction 2 Non-adiabatic correction by scaling vibrational mass,  V 3 Two parameter diagonal correction 4 Full treatment by Schwenke (J. Phys. Chem. A, 105, 2352 (2001).) J. Tennyson, P. Barletta, M.A. Kostin, N.F.Zobov, and O.L. Polyansky, Spectrachimica Acta A, 58, 663 (2002).

Ab initio predictions of water levels Isotopomer N(levels) J(max)  / cm  H 2 16 O H 2 17 O H 2 18 O D 2 16 O HD 16 O All water Rotational non-adiabatic effects very important

Residual sources of error Basis set convergence of MRCI: need extrapolated 7Z Full CI: contributes ~ 1 cm  at 25,000 cm  (?) Surface fitting: 346 points computed, need 1000 points, reduce  by ~ 0.2 cm  Full inclusion of non-adiabatic effects up to 25,000 cm -1